Analysis on Draws: What to Do
with Your Hand?

Pre-Word

The answer to the
question posed in title is the KEY to playing particular hand. In order to win a
player should evaluate chances to finish with particular pattern. (Top 10 wining
patterns you can find here).
And, picking-and-throwing tiles do best to keep alternatives open. At certain
time the decision Where to Go? must be made. Consider, for instance,
typical choices:

·having 5 Pairs is worth to
go for All Pungs or Seven Pairs?,

·having 2/3 Pairs is it worth
to go for All Pungs or any Chow-based hand?

·how many tiles for Knitted
hands is worth to have in order to win?, etc.

First choice is about
to go for Pung-hunt or wait on self-draw. In the second example Chow-based hands
are very flexible though you can pick only from 1 player plus self-draw. The 3rd
strictly suggests self-drawing only until the last tile to pick from anybody.

Approach

Underlying idea to go
through is to use cumulative PROBABILITIES to get certain useful tiles (we
will call them MT = Matching Tiles). Extensive calculations
have been carried out in order to get Number-of-Moves to get (at certain
Level-of-Certainty) required tile depending on starting conditions:
Buying Method, Tiles-in-the-Wall and number of Matching Tiles.
Before those results would be provided let clarify ingredients J.

Table and How to Use It

Here is table for Matching
Tiles (Excel file for convenience is in filter mode). Please, select
values for the fields:

·Method (= Buying
Method),

·Start (=
Tiles-in-the-Wall),

·MT (= Matching
Tiles),

·Prob (=
Level-of-Certainty)

to get expected
number of single moves to get required tile. Lets consider typical CHOICE
problems and try to solve them using attached table.

Example of Choice Problem Solution: 3
Pairs for All Pungs

Lets consider 3
Pairs dealt for the start. How easy is to convert that 2221111111 distribution
for All Pungs? The answer depends on how sure we want to be to get it.
First goes Lucky Guy, cumulative probability = 0.5, which means in
equivalent to pick right tile out of two. (Click here
for full example).

So What?

Analysis listed above
is only a sample of what MAY happen at the table. Real chances highly depend on:

·flexibility of players
strategy,

·portion of luck (Luck
Factor),

·how friendly or not
opponents discards are (Environment Factor).

Transformation Chains Examples

Lets track
transformations of several distributions. For simplicity we assume start of the
hand (83 tiles in the Wall) and couple different Luck Factors.

Rule of Thumb

To estimate
at-the-table when you get next tile toward your hand the following Simplified
Method might be applied.

1.Find
"Tiles-in-the-Wall" number (for instance, 83 for the start of the
game).

2.Find "Matching
Tiles" number.

3.By dividing
"Tiles-in-the-Wall" onto Matching Tiles" you get number of:

single
moves for "Buying Method" = "Full" (Pung, Mah-Jong);

turns
for "Buying Method" = "Draw" (Knitted, Concealed);

HALF
of single moves for "Buying Method" = "Chow" (Chow),
since 2 moves you watch at discards and 2 moves you can act during one turn.

This simplified
formula is valid ROUGHLY for the "Level-of-Certainty" = 70%
which is slightly lower than "Sure" level and much higher than
"Luck" level. To increases "Level-of-Certainty" simply
multiply estimate by 1.1, 1.2 or 1.3.

Small Examples on Rule of Thumb

1.9 Knitted for 10-th tile:
MT=28, 83/28=3 TURNS (Method="Draw");

2.22222111 for a Pair: MT=9,
83/9=9 TURNS;

3.22222111 for Pung, MT=10,
83/10=8 MOVES ("Full") etc.

Whats Next?

It is necessary to
estimate WHEN (meaning how much tiles passed) is good to finish a hand
depending on the hand score. 8 pts. limit for going out increases slightly game
(compared to No Limit rule). Playing level of opponents and their
propensity to compete might give a hint for HOW LONG current hand would be
played. It is crucial to fit within time gap when choosing among the
alternatives. Distribution table of the scores (and Elements) vs. single moves
passed would provide good basis for further analysis.